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Improve examples after meeting

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This commit is contained in:
Patrick Lühne 2020-05-29 12:09:28 +02:00
parent dab121c684
commit b94ee5134a
Signed by: patrick
GPG Key ID: 05F3611E97A70ABF
2 changed files with 5 additions and 6 deletions
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10
examples/example-exact-cover.spec
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@ -4,7 +4,7 @@
# Perform the proofs under the assumption that n is a nonnegative integer input constant. n stands
# for the total number of input sets
input: n -> integer.
#assume: n >= 0.
assume: n >= 0.
# s/2 is the input predicate defining the sets for which the program searches for exact covers
input: s/2.
@ -15,11 +15,11 @@ output: in/1.
# Perform the proofs under the assumption that the second parameter of s/2 (the number of the set)
# is always an integer
#assume: forall X, Y (s(X, Y) -> exists N (Y = N)).
assume: forall Y (exists X s(X, Y) -> exists N (Y = N and N >= 1 and N <= n)).
# Only valid sets can be included in the solution
spec: forall X (in(X) -> X >= 1 and X <= n).
spec: forall Y (in(Y) -> exists N (Y = N and N >= 1 and N <= n)).
# If an element is contained in an input set, it must be covered by all solutions
spec: forall X (exists I s(X, I) -> exists I (in(I) and s(X, I))).
spec: forall X (exists Y s(X, Y) -> exists Y (in(Y) and s(X, Y))).
# Elements may not be covered by two input sets
spec: forall I, J (exists X (s(X, I) and s(X, J)) and in(I) and in(J) -> I = J).
spec: forall Y, Z (exists X (s(X, Y) and s(X, Z)) and in(Y) and in(Z) -> Y = Z).

1
examples/example-prime.spec
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@ -1,7 +1,6 @@
input: n -> integer.
output: prime/1.
# TODO: not necessary if using the lemma below in both directions
assume: n >= 1.
spec: forall X (prime(X) -> exists N (X = N)).